Addressing Node Integration Skewness in Graph Neural Networks Using Hop-Wise Attention

Addressing Node Integration Skewness in Graph Neural Networks Using Hop-Wise Attention | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Addressing Node Integration Skewness in Graph Neural Networks Using Hop-Wise Attention Abdullah Al Thaki, Md Mahmudur Rahman, Md. Mosaddek Khan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6250923/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Graph neural networks (GNNs) often suffer performance degradation as their layer count grows, typically due to the well-known problems of over-smoothing and over-squashing. In this work, we identify an additional factor contributing to this degradation, which we term the K-skewed-traversal problem: certain hop distances are disproportionately emphasized during aggregation, with this emphasis intensifying as the number of layers grows. To address this, we introduce an algorithm called Hop-wise Graph Attention Network (HGAT) that ensures uniform aggregation across hops to eliminate the K-skewed traversal problem, and employs a hop-wise attention mechanism to adaptively prioritize specific hop distances. \textcolor{black}{We theoretically prove that HGAT removes this skewness by balancing contributions from different hop distances before applying hop-wise attention}. Moreover, in our extensive empirical evaluation , we observe notable improvement in terms of solution quality compared to the state-of-the-art GNN models, particularly as the number of layers increases. Optimizing Graph Neural Networks Hop-Wise Attention K-skewed-traversal problem Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6250923","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":430350326,"identity":"ec3ce16a-bd55-4367-80a3-10ba67779a2c","order_by":0,"name":"Abdullah Al Thaki","email":"data:image/png;base64,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","orcid":"","institution":"University of Dhaka","correspondingAuthor":true,"prefix":"","firstName":"Abdullah","middleName":"Al","lastName":"Thaki","suffix":""},{"id":430350327,"identity":"b821c1f9-211a-4bd4-a6e2-6f2186205a16","order_by":1,"name":"Md Mahmudur Rahman","email":"","orcid":"","institution":"University of Dhaka","correspondingAuthor":false,"prefix":"","firstName":"Md","middleName":"Mahmudur","lastName":"Rahman","suffix":""},{"id":430350328,"identity":"cf105d20-2a7b-4917-ba35-267e34c5c830","order_by":2,"name":"Md. 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